**CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 10**

** Section A**

2.Find the number of three-digit natural numbers which are divisible by 11.

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3.Find the distance between the points (o cos 35°, 0) and (0, a cos 55°).

4.A square is inscribed in a circle. What is the ratio of the areas of the circle and the square?

** Section B**

5.A polygon of n sides has n(n-3)/2 diagonals. How many sides has a polygon with 54 diagonals?

6.The sum of first six terms of an AP is 42. The ratio of its 10th term to its 30th term is 1 : 3. Calculate the first term of the AP.

7.If d1 , d_{2} (d_{2} > d1) be the diameters of two concentric circles and c be the length of a chord of a circle which is tangent to the other circle, prove that d2^{2} = c^{2} + d1^{2}.

8.4 face cards of black colour are lost from the pack of 52 playing cards. The remaining cards are well-shuffled and then a card is drawn from them. Find the probability the drawn card is a face card of red colour.

9.Find the area of the largest triangle that can be inscribed in semicircle of radius 14 cm.

10.Volumes of two cubes are in the ratio 8 : 125. What is the ratio of their surface areas?

** Section C**

11.If – 5 is a root of the quadratic equation 2X^{2} + px – 15 = 0 and the quadratic equation p(X^{2}+ x) + k = 0 has equal roots, find the value of k.

13.Show that the sum of first 20 even natural numbers is 21/20 times the sum of first 20 odd natural numbers.

14.Let ABC be a right triangle in which AB = 3 cm, BC = 4 cm and B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

15.Two dice are rolled once. Find two probability of getting such numbers on two dice, whose product is a prime number.

16.At a fete, cards bearing numbers 1 to 400, one on each card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card bears a number which is a perfect square of an even number, the player wins prize. ‘

(i) What is the probability that the first player wins a prize?

(ii) The second player wins prize, if the first has not won

17.Point R divides the line segment joining the points P(3, 2) and Q(6, -7) such that PR/PQ = 1/3. If R lies on the line 3x – 4y + k = 0, find the value of k.

18.The opposite angular points of a square are (1, 0) and (4, 1). Find the coordinates of remaining two vertices of the square.

19.A round table cover has six equal designs as shown in figure. If the radius of the cover is 56 cm, find the cost of making the design at the rate of Rs 5 per cm^{2}.(use root 3=1.7, pi=22/7)

20.The total surface area of solid cylinder is 924 cm^{2}. If the curved surface area is — of its~total surface area,find its radius and height. (Use pi=22/7)

** Section D**

21.One-fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels.

22.If /nth term of an AP is 1/n and nth term is 1/m, show that the sum of mn terms is 1/2(mn + 1).

23.A quadrilateral ABCD is drawn so that D = 90°, BC = 38 cm and CD = 25 cm. A circle is inscribed in the quadrilateral and it touches the sides AB, BC, CD and DA at P, Q, R and S respectively. If BP = 27 cm, find the radius of the inscribed circle.

24.In figure, O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle

at E, find the length of AB.

25.Two circles with centres O and O’ of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and O’P are tangents to the two circles. Find the length of the common chord PQ.

26.The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud from the surface of the lake.

28.If P and Q are two points whose coordinates are (at^{2}, 2at) and((a/t^{2}),(-2a/t)) respectively and S is the point(a,0).show that 1/SP+1/SQ is independent of t.

29.For the inaugration of an Eco-club to the school, badges were given to teachers. Seema made these badges in the shape of an equilateral triangle with a circle of radius root 3 cm inscribed in it as shown in the figure [pi = 3.14]

(a)Find the area of the shaded portion.

(b)Which value is depicted?

30. A godown building is in the form as shown in the figure.

The vertical cross section parallel to the width side of the building is a rectangle of dimensions 7 m x 3 m, mounted by semicircle of radius 3.5 m. The inner measurements of the cuboidal portion of the building are 10 m x 7 m x 3 m. Find the interior surface excluding the floor.

31. An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of base of each of cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight of the pillar, if one cubic cm of iron weighs 10 g. [Use pi = 22/7]

**Answers**

** Section A**

**Ans.**

**2.Find the number of three-digit natural numbers which are divisible by 11.**

**Ans.**

**3.Find the distance between the points (o cos 35°, 0) and (0, a cos 55°).**

**Ans.**

**4.A square is inscribed in a circle. What is the ratio of the areas of the circle and the square?**

**Ans.**

** Section B**

**5.A polygon of n sides has n(n-3)/2 diagonals. How many sides has a polygon with 54 diagonals?**

**Ans.**

**6.The sum of first six terms of an AP is 42. The ratio of its 10th term to its 30th term is 1 : 3. Calculate the first term of the AP.**

**Ans.**

**7.If d1 , d _{2} (d_{2} > d1) be the diameters of two concentric circles and c be the length of a chord of a circle which is tangent to the other circle, prove that d2^{2} = c^{2} + d1^{2}.**

**Ans.**

**8.4 face cards of black colour are lost from the pack of 52 playing cards. The remaining cards are well-shuffled and then a card is drawn from them. Find the probability the drawn card is a face card of red colour.**

**Ans.**

**9.Find the area of the largest triangle that can be inscribed in semicircle of radius 14 cm.**

**Ans.**

**10.Volumes of two cubes are in the ratio 8 : 125. What is the ratio of their surface areas?**

**Ans.**

** Section C**

**11.If – 5 is a root of the quadratic equation 2X ^{2} + px – 15 = 0 and the quadratic equation p(X^{2}+ x) + k = 0 has equal roots, find the value of k.**

**Ans.**

**Ans.**

**13.Show that the sum of first 20 even natural numbers is 21/20 times the sum of first 20 odd natural numbers.**

**Ans.**

**14.Let ABC be a right triangle in which AB = 3 cm, BC = 4 cm and B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.**

**Ans.**

**15.Two dice are rolled once. Find two probability of getting such numbers on two dice, whose product is a prime number.**

**Ans.**

**16.At a fete, cards bearing numbers 1 to 400, one on each card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card bears a number which is a perfect square of an even number, the player wins prize. ‘**

**(i) What is the probability that the first player wins a prize?**

**(ii) The second player wins prize, if the first has not won**

**Ans.**

**17.Point R divides the line segment joining the points P(3, 2) and Q(6, -7) such that PR/PQ = 1/3. If R lies on the line 3x – 4y + k = 0, find the value of k.**

**Ans.**

**18.The opposite angular points of a square are (1, 0) and (4, 1). Find the coordinates of remaining two vertices of the square.**

**Ans.**

**19.A round table cover has six equal designs as shown in figure. If the radius of the cover is 56 cm, find the cost of making the design at the rate of Rs 5 per cm ^{2}.(use root 3=1.7, pi=22/7)**

**Ans.**

**20.The total surface area of solid cylinder is 924 cm ^{2}. If the curved surface area is 2/3 of it’s total surface area,find its radius and height. (Use pi=22/7)**

**Ans.**

** Section D**

**21.One-fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels.**

**Ans.**

**22.If /nth term of an AP is 1/n and nth term is 1/m, show that the sum of mn terms is 1/2(mn + 1).**

**Ans.**

**23.A quadrilateral ABCD is drawn so that D = 90°, BC = 38 cm and CD = 25 cm. A circle is inscribed in the quadrilateral and it touches the sides AB, BC, CD and DA at P, Q, R and S respectively. If BP = 27 cm, find the radius of the inscribed circle.**

**Ans.**

**24.In figure, O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle**

**at E, find the length of AB.**

**Ans.**

**25.Two circles with centres O and O’ of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and O’P are tangents to the two circles. Find the length of the common chord PQ.**

**Ans.**

**26.The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud from the surface of the lake**

**Ans.**

**Ans.**

**28.If P and Q are two points whose coordinates are (at ^{2}, 2at) and((a/t^{2}),(-2a/t)) respectively and S is the point(a,0).show that 1/SP+1/SQ is independent of t.**

**Ans.**

**29.For the inaugration of an Eco-club to the school, badges were given to teachers. Seema made these badges in the shape of an equilateral triangle with a circle of radius root 3 cm inscribed in it as shown in the figure [pi = 3.14]**

**(a)Find the area of the shaded portion.**

**(b)Which value is depicted?**

**Ans.**

**30. A godown building is in the form as shown in the figure.**

**The vertical cross section parallel to the width side of the building is a rectangle of dimensions 7 m x 3 m, mounted by semicircle of radius 3.5 m. The inner measurements of the cuboidal portion of the building are 10 m x 7 m x 3 m. Find the interior surface excluding the floor.**

**Ans.**

**31. An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of base of each of cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight of the pillar, if one cubic cm of iron weighs 10 g. [Use pi = 22/7]**

**Ans.**

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